# Prove that the angle formed by a chord in a major segment is acute?

1
by vimalSuresh

2015-05-09T12:07:28+05:30
Given :-

⇒ In the given circle , the following things should be noted-

⇒ O is the centre of the circle

⇒ AB is the chord .

⇒ ACB is the major sector { Because  it lies in the larger portion of the circle }

⇒ADB is he minor sector   { As it lies in the smaller portion of the circle          }

TO PROVE ;-

⇒''Prove that the angle formed by a chord in a major segment is acute''

PROOF :-

We know that  ∠ACB is one of the angle of the major sector.

So remember the theorem :- ''
The angle subtended by an arc of a circle at its centre is twice the angle subtended by it at any point on the remaining circle''

⇒ Hence by this above statement we get as ,

AOB = 2∠ACB  { where ACB is the major sector and ACB is the angle subtended by it in another segment. }

Hence ,

2∠ACB < 180°

⇒ We get the result as  ∠ACB < 90°

⇒So hence ∠ACB is an acute angle because it is lesser than 90 degree.

Hence proved.

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